Over the last few decades, with the increasingly accurate positioning services (e.g., GPS, AIS, Mobile Phone Triangulation, RFID/Wi-Fi tracking, etc.) and the decreasing price of their deployment, locational data is becoming pervasive in our daily lives and scientific researches. Either indoor or outdoor, it is not difficult to obtain the trace, the velocity, and even the acceleration of any moving entity (referred to as an “object” herein) of interest with proper equipment and infrastructure. Massive data have been collected in various research projects since the early 90's. As part of the “big data regime,” interest in locational data has recently grown even more rapidly due to advancement in database technology and data mining techniques.
When locational data is coupled with time-stamps, it becomes spatial-temporal data, having both space (spatial) and time (temporal) information. The timely sequence of locations of an object defines its trajectory. Trajectories of objects are widely used in a variety of business and public sector applications, such as traffic modeling and supply chain management. More often, they are important sources for mobility observation, a process in which information related to objects' movement, such as patterns, correlations, and clusters, can be discovered.
While pervasive positioning technologies provide opportunities to access vast amount of locational data and test these solutions, they also raise challenges due to the sparse nature of data collection strategies, the diverse density of the data, and technical issues associated with the accuracy of the data. The enormous volume of data can easily overwhelm human analysis. This is sometimes solved by a compression algorithm, for example. However, source data can often be inaccurate and inconsistent.
In general, existing mobility observation techniques can be classified as one of the following three categories:                State Based: states are defined by (time, location) combinations. The trajectory of an object is a sequence of states and the transitions among them. Markov-chain and other related models can be used to study the underlying patterns.        Similarity Based: similarity between trajectories can be calculated from the 3-dimensional or 4-dimensional proximity of the data points. It is then usually used to define clusters or places of interest.        Density Based: in large scale problems, importance of locations can simply be reflected by the density of data points in that area.        
However, these solutions all have weaknesses when dealing with different data sets. For example, if the data points are scarce (either spatially or temporally), the similarity based solution may produce inaccurate results, because data points for similar trajectories may be far apart. On the other hand, for high frequency locational data (e.g. continuously generated by positioning sensors), the state based approach could be overwhelmed by the enormous number of states. Compression algorithms are often needed to pre-process the data and could result in inefficiency. Also, the density based solutions will often need the timely frequency of data points to be normalized; otherwise their density would not reflect the true distribution of the moving objects.
Moreover, it is not common for existing solutions to deal with the error in the location detections, which in fact could be crucial to the correctness of the results. Hence, current solutions generally do not have the ability to adapt to different source locational data, and to extract as much useful information from the data.